TMUA 2017 · Paper 1 · Question 17

The two functions $F (n)$ and $G (n)$ are defined as follows for positive integers $n$ :

F (n) = \frac{1}{n} \int_{0}^{n} (n - x) d x

G (n) = r = 1 \sum n F (r)

What is the smallest positive integer $n$ such that $G (n) > 150$ ?